Labour, Liberal Democrat and DUP MPs have all backed British air strikes against Islamic State (Isis) targets in Syria in today's all-day debate in the House of Commons.

High-profile Labour backbenchers, including former shadow home secretary Yvette Cooper and former deputy Labour leader Margaret Beckett, have said they will vote in favour of the government's proposals for military intervention in Syria, as have Liberal Democrat leader Tim Farron and DUP leader Nigel Dodds.

MPs have already been debating the issue for more than four hours, and are expected to continue the back-and-forth until a vote at about 10PM tonight. John Bercow, the speaker of the House of Commons, said at the start of the debate that 157 MPs had asked to speak.

The majority of MPs are expected to vote in favour of the government's motion, despite fierce opposition from Labour leader Jeremy Corbyn and others in both the Labour and Conservative parties. In 2013, 30 Tory MPs voted against the then-government's proposals for joining a US military operation against the Assad regime.

Prime Minister David Cameron opened the debate this morning, but repeatedly came under fire from multiple MPs questioning media reports that he urged his Conservative colleagues late last night not to vote with Labour leader Jeremy Corbyn and a "bunch of terrorist sympathisers".

Cameron did not apologise directly for the alleged comments, but told MPs: "I respect people who come to a different view.

"I respect people who disagree. I respect the fact that governments of all colours have had to fight terrorism."

Calling Isis "Daesh" rather than the Islamic State, the militant group's preferred name, Cameron said today's vote is "about how we fight terrorism, not whether we fight terrorism" and that there would be "honour" in voting for or against the government's proposals.

In his response to Cameron during today's debate, Corbyn said the Prime Minister’s comments "both demeans the office of the Prime Minister and undermines the seriousness of the deliberations we are having today".

Corbyn, who is allowing Labour MPs to have a "free vote" but will vote against further military intervention, said Cameron's proposal "simply doesn’t stack up".

"The logic of an extended air campaign is mission creep and western boots on the ground, whatever the Prime Minister may say now," Corbyn said.

The motion MPs are debating would authorise British air strikes in Syria. Cameron has insisted no British ground troops would be involved in the mission.

In his comments earlier, Cameron said that the government had launched a new comprehensive review to eliminate the funding of extremist groups in the UK and would be issuing a report on the matter next week.

Fewer than half of British voters support a British bombing campaign in Syria, according to a new YouGov survey published in the Times newspaper this morning. YouGov found that support for the extension had slipped from 59 per cent to 48 per cent since Cameron first set out his case for further air strikes last week.